“We don’t like picking 19,’’ Reese said. “That is early for us. We hate picking this high.’’

Sitting at No. 19 is 13 spots higher than the Giants general manager wants to be. A year ago, Reese was thrilled to take running back David Wilson with the 32nd pick in the first round. Last is the place to be because that means you won the Super Bowl the previous year. This time, the Giants select near the middle of the first round, an appropriate landing spot for a 2012 team that bumped along at 9-7 to finish just out of the playoffs.

“Hopefully we can get a player who can come in — I always say this [about] your first three picks — you want those guys to come in and contribute for you right away,’’ Reese said. “Hopefully you will get a couple of starters out of them. So hopefully we will get a good player at 19. I think we will.’’

Anyone who caught just a glimpse of the Giants last season realizes they need help on defense, after finishing 31st in the league and setting a franchise record for most yards allowed. A strong case can be made the Giants are in need of upgrades at linebacker and cornerback and even at defensive end, once a position overflowing with talent.

The Giants did a good job in free agency solidifying themselves at defensive tackle, signing former Eagles Cullen Jenkins and Mike Patterson and taking a gamble with little downside by re-signing massive veteran Shaun Rogers. They signed tight end Brandon Myers to replace Martellus Bennett, who went to the Bears. But there’s work to be done to spruce up the talent base.

At the moment, the starting right tackle is David Diehl, a 10-year veteran who remains on the roster because he agreed to a hefty pay cut. Diehl lost his job last season to Sean Locklear and is coming off arthroscopic right knee surgery. The Giants would like to squeeze another year out of Diehl, because third-year tackle James Brewer is unproven in reserve. If D.J. Fluker of Alabama is sitting there at No. 19, it would represent a perfect need/value selection, because the massive, 339-pound Fluker is considered to be ready to step in and start immediately.

The Giants haven’t taken a linebacker in the first round since 1984, when they took Carl Banks out of Michigan State then sat back and enjoyed his work for nearly a decade. There certainly is a reason to add a linebacker, though former Panther and Cowboy Dan Connor was signed to a one-year contract to replace Chase Blackburn, who got a two-year deal from the Panthers.

The Giants are under no illusion that Connor is a difference-maker, but it would be a surprise if they take a linebacker in the first round, given they usually do not value this position as highly as others on defense (defensive end, cornerback).

Manti Te’o of Notre Dame should be there at No. 19 and wouldn’t it cause a stir if the Giants took this highly-decorated player who attracted

national attention and ridicule/empathy for getting “catfished’’ with an imaginary dead girlfriend. Alec Ogletree of Georgia is an intriguing athlete, but he has long rap sheet.

Even though Jason Pierre-Paul and Justin Tuck return as starters and Mathias Kiwanuka is moving back from outside linebacker back to his natural position, expect the Giants to add a defensive end sometime in the early rounds. If the Giants scouts believe Bjoern Werner of Florida State is a future star, he would be worth the investment at No. 19.

There always is a desire to put as many capable cornerbacks on the team as possible. Corey Webster, a steady player and starter on two Super Bowl defenses, slumped badly in 2012 and returns only because he agreed to a cut in pay. If the Giants deem someone such as Desmond Trufant from Washington as a top prospect at corner, they will take him.